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AlgebraQuestion and Answers: Page 299

Question Number 65457 Answers: 1 Comments: 0

{ (((a/b)+((b−a)/(b+a))=2(√3))),(((b/a)+((b+a)/(b−a))=3(√2))) :} [a,b∈R,a≠b]

Question Number 65347 Answers: 1 Comments: 0

Question Number 65271 Answers: 1 Comments: 0

x^4 +ax^2 +bx+c=0 solve for x.

$${x}^{\mathrm{4}} +{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$${solve}\:{for}\:{x}. \\ $$

Question Number 65227 Answers: 0 Comments: 3

Question Number 65198 Answers: 0 Comments: 5

let a∈R^+ , and x>0 x^4 +(1−2a)x^2 −2ax+1=0 find x

$${let}\:{a}\in\mathbb{R}^{+} \:,\:{and}\:{x}>\mathrm{0} \\ $$$${x}^{\mathrm{4}} +\left(\mathrm{1}−\mathrm{2}{a}\right){x}^{\mathrm{2}} −\mathrm{2}{ax}+\mathrm{1}=\mathrm{0} \\ $$$${find}\:{x} \\ $$

Question Number 65087 Answers: 1 Comments: 0

Question Number 65115 Answers: 1 Comments: 0

x^x =64 find x

$$\mathrm{x}^{\mathrm{x}} =\mathrm{64} \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$

Question Number 65114 Answers: 0 Comments: 0

x^x^(lnx) =64 find x

$$\mathrm{x}^{\mathrm{x}^{\mathrm{lnx}} } =\mathrm{64} \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$

Question Number 65062 Answers: 1 Comments: 5

If x^4 +ax^2 +bx+c=0 ⇒ t^4 +At^2 +B=0 Find A and B.

$${If}\:\:{x}^{\mathrm{4}} +{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$\Rightarrow\:{t}^{\mathrm{4}} +{At}^{\mathrm{2}} +{B}=\mathrm{0} \\ $$$${Find}\:{A}\:{and}\:{B}. \\ $$

Question Number 65054 Answers: 2 Comments: 2

{ (((√(x+y))+(√(x−y))=a)),((x^2 +y^2 =b [a,b∈R])) :}

$$\begin{cases}{\sqrt{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}}+\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}}=\boldsymbol{\mathrm{a}}}\\{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\boldsymbol{\mathrm{b}}\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\boldsymbol{\mathrm{R}}\right]}\end{cases} \\ $$

Question Number 64867 Answers: 1 Comments: 0

x^4 +(2i−3)x^3 −(1+6i)x^2 +(3−2i)x−2=0

$${x}^{\mathrm{4}} +\left(\mathrm{2}{i}−\mathrm{3}\right){x}^{\mathrm{3}} −\left(\mathrm{1}+\mathrm{6}{i}\right){x}^{\mathrm{2}} +\left(\mathrm{3}−\mathrm{2}{i}\right){x}−\mathrm{2}=\mathrm{0} \\ $$

Question Number 64837 Answers: 1 Comments: 0

{ ((x^(√y) + y^(√x) = ((49)/(48)))),(((√x) + (√y) = (7/2))) :} find x and y

$$\begin{cases}{{x}^{\sqrt{{y}}} \:+\:{y}^{\sqrt{{x}}} \:=\:\frac{\mathrm{49}}{\mathrm{48}}}\\{\sqrt{{x}}\:+\:\sqrt{{y}}\:=\:\frac{\mathrm{7}}{\mathrm{2}}}\end{cases} \\ $$$$ \\ $$$${find}\:{x}\:{and}\:{y} \\ $$$$ \\ $$

Question Number 64758 Answers: 2 Comments: 0

Solve: x^4 + 5x^3 − 4x^2 + 7x − 1 = 0

$$\mathrm{Solve}:\:\:\:\:\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{5x}^{\mathrm{3}} \:−\:\mathrm{4x}^{\mathrm{2}} \:+\:\mathrm{7x}\:−\:\mathrm{1}\:\:=\:\:\mathrm{0} \\ $$

Question Number 64631 Answers: 1 Comments: 3

(√((1+2x(√(1−x^2 )))/2))+2x^2 =1 To solve in R

$$\sqrt{\frac{\mathrm{1}+\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\mathrm{2}}}+\mathrm{2}{x}^{\mathrm{2}} =\mathrm{1} \\ $$$$\mathrm{To}\:\mathrm{solve}\:\mathrm{in}\:\mathbb{R} \\ $$

Question Number 64604 Answers: 0 Comments: 0

find all integr naturals n and k wich verify k!=(2^n −1)(2^n −2)(2^n −4)...(2^n −2^(n−1) )

$${find}\:\:{all}\:{integr}\:{naturals}\:{n}\:{and}\:{k}\:{wich}\:{verify} \\ $$$${k}!=\left(\mathrm{2}^{{n}} −\mathrm{1}\right)\left(\mathrm{2}^{{n}} −\mathrm{2}\right)\left(\mathrm{2}^{{n}} −\mathrm{4}\right)...\left(\mathrm{2}^{{n}} −\mathrm{2}^{{n}−\mathrm{1}} \right) \\ $$

Question Number 64580 Answers: 3 Comments: 0

a^2 +b^2 =a+b ,a^2 −b^2 =ab a=? b=? and what if a^2 +b^2 =a−b?

$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={a}+{b}\:,{a}^{\mathrm{2}} −{b}^{\mathrm{2}} ={ab} \\ $$$${a}=?\:{b}=? \\ $$$${and}\:{what}\:{if}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={a}−{b}? \\ $$

Question Number 64542 Answers: 2 Comments: 0

Question Number 64519 Answers: 1 Comments: 0

a,b,c is a geometric progression such that a+b+c=26 a^2 +b^2 +c^2 =364 find a,b,c

$${a},{b},{c}\:{is}\:{a}\:{geometric}\:{progression}\:{such} \\ $$$${that} \\ $$$${a}+{b}+{c}=\mathrm{26} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{364} \\ $$$$ \\ $$$${find}\:{a},{b},{c} \\ $$

Question Number 64508 Answers: 2 Comments: 1

factorize (x+1)(x+3)(x+5)(x+7)+16

$$\mathrm{factorize}\:\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}+\mathrm{3}\right)\left(\mathrm{x}+\mathrm{5}\right)\left(\mathrm{x}+\mathrm{7}\right)+\mathrm{16} \\ $$

Question Number 64475 Answers: 2 Comments: 6

solve the equation sin(x)+sin(2x)+sin(3x)=cos(x)+cos(2x)+cos(3x)

$${solve}\:{the}\:{equation} \\ $$$${sin}\left({x}\right)+{sin}\left(\mathrm{2}{x}\right)+{sin}\left(\mathrm{3}{x}\right)={cos}\left({x}\right)+{cos}\left(\mathrm{2}{x}\right)+{cos}\left(\mathrm{3}{x}\right) \\ $$

Question Number 64447 Answers: 1 Comments: 0

Question Number 64404 Answers: 0 Comments: 4

Question Number 64378 Answers: 0 Comments: 1

Question Number 64284 Answers: 0 Comments: 0

Find all the integer solution 3x^2 + 1 = 4y^3

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{solution}\:\:\:\:\:\:\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{1}\:\:=\:\:\mathrm{4y}^{\mathrm{3}} \\ $$

Question Number 64187 Answers: 1 Comments: 0

Question Number 64186 Answers: 1 Comments: 0

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